One World Trade Center, left, and 4 World Trade Center, right, are part of the ongoing construction at Ground Zero.

In a word, the redevelopment of the World Trade Center is complicated.

There’s a tangled web of owners and different towers rising at the same time, all on a compact site.

One of the best vantage points for this complexity belongs to Tishman Construction, the New York-based builder that has overseen construction at many of New York’s largest towers, including Goldman Sachs Group’s new building and the Bank of America tower in Midtown.

Owned by AECOM, Tishman is the construction manager for One World Trade Center (owned by the Port Authority of New York and New Jersey and the Durst Organization); it’s co-construction manager on the Santiago Calatrava-designed $3.4 billion transportation hub (owned by the Port Authority); and it’s building 3 and 4 World Trade Center (owned by Silverstein Properties). Construction on 3 World Trade Center will stop at seven stories if Silverstein doesn’t find a tenant.

Mike Mennella oversees all these projects for Tishman, and took time last week to chat about building One World Trade — slated to be the country’s tallest building — and the other projects.

WSJ: How long have you been involved in this?

Mr. Mennella: I’ve been involved in the site since literally the day after 9/11. … Back in 2001, Tishman had a previous relationship with Larry Silverstein.

WSJ: On Tower One, how high up are you right now?

Mr. Mennella: One hundred stories, passing the height of the Empire State Building on a structural basis in the next week or so, and on the way to 105. We’ll top out at 105 in the very near future, and we’ll go to the antenna above that.

WSJ: Is it a challenge to add on the spire – how do you get it up there?

Mr. Mennella: It’s all been pre-planned from Day One. The cranes that were on the site were picked to raise that tower in pieces, at their maximum constructed weight. … Each segment of the tower will max out at 52 tons.

WSJ: Besides the antenna, what are some challenges with building up so high? I know you’ve had some wind delays.

Mr. Mennella: The cranes shut down in excess of 30 miles per hour, and we’ve lost several weeks during the winter — not because of snow, not because of anything except wind. … The job did slow down — it looks lovely, the sun’s out, but the wind up there is pretty rough, so it’s been interesting.

WSJ: What about the construction makes (One World Trade) so expensive?

Mr. Mennella: The building has enhancements that are very special because of the nature of the building: The height, the security of the building, the location, the amount of concrete sitting on top of the train—the PATH train, the track that runs to New Jersey runs right through the core of that building at the bottom of that building

WSJ: On 3 World Trade Center, you’re building the podium, which is seven stories, right?

Mr. Mennella: We’re building the building that can stop at seven stores if necessary. It can continue on, and we’ve bought the project up to its roof.

WSJ: Meaning, you’ve ordered all the materials for the whole building?

Mr. Mennella: We’ve bought all the contracts for the entire building. We are staging the materials based on our instructions from the client.

WSJ: Of the three projects, the Silverstein towers, the transportation hub and One World Trade, which is the most complex to build?

Mr. Mennella: It’s no question — Tower One is a challenge, but the transportation hub — the Calatrava type of project — is challenging. … The detailing of the steel, the nature of the structure is very, very architectural — it’s actually artistic, so it has very unique installation difficulties. The equipment is difficult… the heaviest pieces of steel have been in the hub.

WSJ: How big?

Mr. Mennella: 100 ton-plus.

WSJ: Do you get put in a funny position when the Silverstein folks and the Port Authority folks fight at various times of the project?

Mr. Mennella: We’ve had Tishman people on both sides of the table during the arbitration and we managed to keep everyone not mad at me. … I have often sat at the end of the table — in the middle—with the Port Authority on one side and Silverstein on the other, and tried to moderate and mediate. … We continue to get assignments because we have, I think, approached it so rationally or fairly.

(This interview has been edited for clarity and length.)

Corrections & Amplifications: An earlier version of this post misspelled Mr. Mennella’s last name as Manella.